UNIVERSITY OF TECHNOLOGY, SYDNEY
Efficient Algorithms and a Two-Stage
Framework for Autonomous Exploration
of Complex 3D Environments Using a
Climbing Robot
by
Phillip Quin
A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy
in the
Faculty of Engineering and IT Intelligent Mechatronic Systems Group
Declaration of Authorship
I, Phillip Quin , declare that this thesis titled, ‘Efficient Algorithms and a Two-Stage Framework for Autonomous Exploration of Complex 3D Environments Using a Climbing Robot’ and the work presented in it are my own. I confirm that:
This work was done wholly or mainly while in candidature for a research degree at
this University.
Where any part of this thesis has previously been submitted for a degree or any
other qualification at this University or any other institution, this has been clearly stated.
Where I have consulted the published work of others, this is always clearly attributed. Where I have quoted from the work of others, the source is always given. With the
exception of such quotations, this thesis is entirely my own work.
I have acknowledged all main sources of help.
Where the thesis is based on work done by myself jointly with others, I have made
clear exactly what was done by others and what I have contributed myself.
Signed:
Date:
UNIVERSITY OF TECHNOLOGY, SYDNEY
Abstract
Faculty of Engineering and IT Intelligent Mechatronic Systems Group
Doctor of Philosophy
iii
Enabling robots to autonomously explore complex 3D environments is crucial in facilitating the automation of many real-world tasks. There exist many algorithms for exploring unknown environments with autonomous robots. Most of these are restricted to the 2D case, or to cases where the robot can be abstracted as a holonomic point robot. Algorithms that deal with the 3D case restrict the robot’s possible positions to the 2D plane, or assume that the robot can freely move through any empty space, like an idealised quadrocopter. This thesis presents a two-stage exploration framework that allows robots to consider any adherable surface in a 3D environment as a potential position from which to conduct exploration. The framework is therefore suitable to any robotic platform that must at all times maintain contact with a surface, but where this surface need not be the floor plane. A Nearest Neighbours Exploration Approach (NNEA) is developed to accomplish explo-ration of the environment immediately surrounding the robot when the robot is fixed to a position on a surface. In this approach, the Next Best Viewpoint is selected first by evaluating and choosing between candidate viewpoints that are within a bounded range of the robot’s current position. NNEA is demonstrated in experiments in a real bridge environment for the case of a high degrees of freedom (DOF) robot arm with a fixed base. NNEA is shown to result in faster exploration times in the case of a high-DOF robot arm in a fixed base position.
Four frontier detection algorithms are proposed and investigated for determining the set of frontiers—the boundary between known and unknown space—after each map update. The resulting frontiers are used to limit which candidate positions need to be considered for exploration. The novel frontier detection algorithms are compared to other state of the art algorithms and are found to be suited for efficient frontier detection in different situations.
A novel graph-based method for selecting the Next Best Base location (NBB) is presented in which the map is used to create an updated graph of possible positions for the robot base, sampled from all surfaces. Positions that are sufficiently close to the frontiers are selected as candidate positions for the robot to move to next. The information that could be gained from each reachable candidate position is estimated. A cost function determines which candidate is the best to move to next, and the robot moves to that position to take
iv
another sequence of scans. This method is demonstrated in simulations and experiments to be efficient in minimising the computation required to select and move to the NBB. The exploration framework and the developed algorithms and approach are demonstrated in simulation in an environment made up of unconnected surfaces, large enough that the robot is required to repeatedly move through the environment in order to fully explore it. The framework is shown to result in efficient exploration of the observable environment.
Acknowledgements
If you want to build a ship, don’t drum up people together to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea.
— Antoine de Saint-Exup´ery
I would like to thank my supervisor Professor Dikai Liu for providing guidance and support, particularly when it came to the bigger picture of the thesis, and for making it possible to be a part of the Bridge Climbing Robot project through the ARC linkage grant and in collaboration with the Roads and Maritime Services NSW.
I am also grateful to all the staff and students at the Centre for Autonomous Systems (CAS) for providing a warm and supportive environment for research. The Bridge Climbing Robot project of which my thesis is a part would not have been as interesting, entertaining or feasible without the participation of many others, including Peter Ward, David Pagano, Chia-Han “John” Yang, and Liyang Liu.
I owe a lot to my co-supervisors Dr. Alen Alempijevic and Dr. Gavin Paul. Gavin gave me the tools to get started, and both spent many hours reading and giving feedback on my work, papers, and presentations. If ever I was stuck or at a mental dead-end, I could be sure that explaining my train of thought to Alen or Gavin, and our subsequent discussions, would result in some new insight. When I grow up, I want to be as helpful and reliable as they are to those around them. Hvala and to both of you for being my when bio sam mlad i okean bilo duboko.
My parents instilled in me a love of science, engineering, and discovery. More dubiously, they gave me the confidence to take up the offer of a PhD scholarship in the first place.
Mais petit a petit, l’oiseau fait son nid, and they followed through by giving me the support
and confidence to see the thesis through to the end, otherwise I might never have forgiven them.
Thanks go to my brother Adam, for being fun to hang out with, when that was exactly what I needed, and to my brother Eric, for making me want to become a doctor before he did (I lost); even if we might argue about what a “real” doctor is.
To all my friends I am indebted for helping me maintain some modicum of stability and perspective when I otherwise would have been overwhelmed. Thanks for being fun people to spend time with.
vi
To Glenn Shea, Carrie Browne, and Mitesh Patel, for having been-there-done-that, Helen Fearnley for being a trailblazer, and Maximilian Wittmann for proving that even PhDs come to an end. Particular thanks to Denny Krstevski, for keeping me engaged in artistic
pursuits. To Tom Hsu, 感谢您提供住房和酒精.
To Andrija Krstic, for being so large in life and in the memories of his loved ones that he is able to inspire someone who will never have the pleasure of meeting him. From him I hope I’ve at least learnt xto moex danas, ne ostavljaj za sutra.
Finally, Nevenka Krstic, moje svetlo u oluji. This thesis would not have happened without you.
Contents
Declaration of Authorship iii
Abstract iv
Acknowledgements vii
List of Figures xiii
List of Tables xvii
Abbreviations xix
Nomenclature xxi
Glossary of Terms xxv
1 Introduction 1
1.1 Background and Motivation . . . 4
1.2 Research Questions . . . 8
1.3 Scope . . . 9
1.4 Contributions . . . 10
1.5 Publications . . . 11
1.5.1 Directly Related Publications . . . 11
1.5.2 Related Publications . . . 12
1.6 Thesis Outline . . . 12
2 Review of Related Work 15 2.1 Mapping and Localisation in Complex 3D Environments . . . 16
2.1.1 Metric Representations . . . 16
2.1.2 Topological Representations . . . 20
2.1.3 Simultaneous Localisation and Mapping (SLAM) . . . 21
2.2 Path Planning and Collision Avoidance . . . 22
2.3 Exploration: Semi-Autonomous vs. Autonomous . . . 25
2.4 Exploration: Targets, Known Environments, and Undirected Strategies . . . 27 vii
CONTENTS viii
2.4.1 Searching for a Target in Known Environments . . . 27
2.4.2 General Exploration in Known Environments . . . 27
2.4.3 Undirected Exploration . . . 29
2.5 Exploration: Directed Investigation of Unknown Space . . . 31
2.5.1 Wall-Following . . . 32
2.5.2 Exploration as Path Planning By-Product . . . 32
2.5.3 Next Best View Exploration . . . 33
2.5.4 Utility and Frontier Based Exploration . . . 34
2.5.5 Graph-Based Exploration . . . 38
2.5.6 C-space Based Exploration . . . 40
2.5.7 Exploration Termination Criteria . . . 42
2.6 Summary . . . 43
3 Two-Stage Exploration Framework 47 3.1 Description . . . 49
3.1.1 Local Exploration . . . 49
3.1.2 Determining and Moving to the Next Best Base Location . . . 51
3.2 Conclusions . . . 52
4 Nearest Neighbour Exploration Approach 53 4.1 Overview . . . 53
4.2 Nearest Neighbour Exploration Approach . . . 56
4.2.1 Finding Nearest Neighbour NBV . . . 56
4.2.2 Sampling all C-space for NBV . . . 60
4.2.3 Nearest Neighbour Exploration Approach with Backtracking . . . . 62
4.3 Complexity of Calculations . . . 65
4.4 Experiments and Simulations . . . 70
4.4.1 Robot and Environment . . . 70
4.4.2 Experiment Design . . . 72
4.4.3 Results . . . 74
4.5 Engineering Challenges . . . 80
4.5.1 Sensor Minimum Range . . . 80
4.5.2 Managing Occlusion of Sensor FOV by the Robot . . . 81
4.5.3 Deflection of Robot Joints Due to Gravity . . . 82
4.6 Discussion . . . 82
4.6.1 Quality of Environments Used . . . 83
4.6.2 Estimation of Possible Information Gain . . . 83
4.6.3 Analysis of Maximal Effort as a Predictor of Time Spent in Motion . 86 4.6.4 Choosing Information Thresholds . . . 88
4.7 Conclusions . . . 88
5 Frontier Detection Algorithms 91 5.1 Nomenclature . . . 92
5.2 Na¨ıve Active Area Frontier Detection . . . 93
CONTENTS ix
5.2.2 Soundness and Completeness . . . 94
5.2.3 Analysis . . . 94
5.3 Expanding Wavefront Frontier Detection . . . 95
5.3.1 Description . . . 96
5.3.2 Soundness and Completeness . . . 97
5.3.3 Algorithm Analysis . . . 98
5.4 Frontier-Tracing Frontier Detection . . . 101
5.4.1 Description . . . 103
5.4.2 Soundness And Completeness . . . 105
5.4.3 Analysis . . . 106
5.5 State-Based Frontier Detection . . . 108
5.5.1 Analysis . . . 112 5.6 Experiments . . . 113 5.6.1 Design . . . 113 5.6.2 Results . . . 114 5.7 Discussion . . . 121 5.7.1 Summary of Complexity . . . 121
5.7.2 Choosing a Frontier Detection Approach . . . 123
5.8 Conclusions . . . 124
6 A Graph-Based Method for Selecting the Next Best Base Location 127 6.1 Description . . . 127
6.1.1 Determining Attachment Points . . . 129
6.1.2 Estimating Candidate Information Score . . . 132
6.1.3 Selecting and Moving to the Next Best Base Location . . . 132
6.2 Analysis . . . 136
6.3 Experiments . . . 139
6.4 Discussion . . . 141
7 Case Study: Exploration of Multi-Surface Environments 147 7.1 Experiment Design . . . 148
7.1.1 The Environment and the Robot . . . 148
7.1.2 System Implementation . . . 149
7.1.3 Evaluation Criteria . . . 150
7.2 Results . . . 152
7.3 Discussion . . . 156
7.3.1 The Utility Function . . . 156
7.3.2 Execution Time . . . 158
7.3.3 m-A*, Connectivity, and Edge Validity . . . 162
8 Conclusions 163 8.1 Summary of Contributions . . . 164
8.1.1 A Two-Stage Exploration Framework for Climbing Robots . . . 164
8.1.2 A Novel Manipulator-Based Exploration Approach . . . 164
CONTENTS x
8.1.4 A Graph-Based Method for Selecting the Next Best Base Location . 165
8.1.5 Practical Contribution . . . 166
8.2 Discussion of Limitations . . . 166
8.3 Future Work . . . 167
Appendices 169 A NNEA Experimental Data 171 A.1 Exploration Metrics . . . 171
A.2 Time Profiles . . . 174
B Existing Frontier Detection Algorithms 177 B.1 Na¨ıve Frontier Detection . . . 178
B.2 Wavefront Frontier Detection . . . 178
B.3 Fast Frontier Detection . . . 179
B.4 Incremental Wavefront Frontier Detection . . . 182
C Frontier Detection Experimental Data 185 C.1 Environments and Trajectories . . . 185
C.2 Total Time and Operations . . . 187
C.3 Computation Per Iteration Over Time . . . 189
C.4 Trend Analysis . . . 192
C.5 Tables . . . 192
List of Figures
1.1 Skycleaner 3, Hulltimo, and Expliner. . . 4
1.2 Bridge inspectors in Canada. (Credit: CRAS) . . . 6
1.3 Bridge inspectors in Missouri, USA. (Credit: MoDOT, KBIA) . . . 6
1.4 The caterpillar-inspired 7DOF robot platform. . . 7
2.1 An occupancy grid. . . 17
2.2 A laser return being incorporated into an occupancy grid. . . 18
2.3 A multi-level surface map. . . 18
2.4 A quadtree structure. . . 19
2.5 A floorplan and a topological map. . . 21
2.6 A Voronoi graph built from an environment. . . 21
2.7 Ellipsoids used to detect and prevent collisions. . . 25
2.8 Camera placements in an art gallery [1]. . . 28
2.9 Asymptoticall optimal coverage planner. . . 29
2.10 Demonstration that exploration of unknown environments can only be greedy. 30 2.11 A Levy walk. . . 31
2.12 Following walls to travel through the environment. . . 32
2.13 Exploration as a by-product of path planning. . . 33
2.14 Frontier cells. . . 36
2.15 A potential field and harmonic function. . . 37
2.16 Exploration using SRT-Ball and SRT-Star. . . 39
2.17 Reducing C-space entropy. . . 41
2.18 Thresholds for ending exploration. . . 42
2.19 Getting stuck when moving the sensor towards frontiers. . . 44
2.20 Regions missed when only considering ground plane. . . 45
3.1 The two-stage exploration framework. . . 48
3.2 Example configurations from a local exploration strategy. . . 50
3.3 Attachment points as nodes in a graph. . . 51
4.1 A sequence of greedy optimal observations. . . 55
4.2 The robot “painting itself into a corner”. . . 56
4.3 The Nearest Neighbours Exploration Approach. . . 57
4.4 Choosing Δθ based on the discretisation ofP. . . 59
4.5 Nearest Neighbours Exploration Approach with Backtracking. . . 63
4.6 The tree T of poses generated by NNEA-B. . . . 64 xi
LIST OF FIGURES xii
4.7 The number of evaluations required by an optimal planner and NNEA. . . . 66
4.8 The percentage of calculations saved by NNEA. . . 68
4.9 Values of m and k for which NNEA and NNEA-B are worthwhile. . . . 69
4.10 The robot in the simulated environments. . . 71
4.11 The robot in the lab and bridge environments. . . 72
4.12 Performance in simulated environments. . . 74
4.13 Performance in lab and bridge environments. . . 75
4.14 Meshes resulting from exploration. . . 76
4.15 Time taken by each task in the lab and bridge environments. . . 77
4.16 Information over time. . . 79
4.17 Joint deflection and managing unknown cells within minimum range. . . 81
4.18 Filling in free space when receiving 0 range reading. . . 81
4.19 (a) Bridge site 1 and (b) bridge site 2 seen from the side. . . 83
4.20 Estimating information as a function of the number of sensor observations. 85 4.21 Estimating the maximum observable information as a function of |Qa|. . . . 86
4.22 Maximal effort vs. movement time. . . 87
4.23 Choosing between Local Exploration algorithms. . . 89
5.1 Cells inPfreet − Pfreet−1 which will be evaluated at time t. . . . 98
5.2 The cells evaluated by FTFD and EWFD. . . 102
5.3 Relationships between the sensor FOV and frontiers. . . 102
5.4 An example of how a pocket could form. . . 103
5.5 A cell/voxel and its neighbours in an occupancy grid. . . 110
5.6 The Cave and Freiburg simulated environments. . . 113
5.7 Comparison of each algorithm’s running time. . . 116
5.8 Computation time at each iteration in Freiburg trajectory H. . . 117
5.9 Computation time of frontier detection vs. number of known freespace cells. 118 5.10 Preliminary experiments using real 2D data. . . 120
6.1 A flowchart of processes involved in the exploration strategy. . . 128
6.2 Example attachment positions. . . 129
6.3 Two attachment positions. . . 130
6.4 Attachment nodes and the edges between them. . . 131
6.5 Methods for estimating information gain. . . 133
6.6 The robot moving through a simple plank environment. . . 140
6.7 The robot in the beams environment, consisting of three disjoint surfaces. . 142
6.8 The robot in the box environment, consisting of four surfaces. . . 143
6.9 The robot in the lab rig. . . 144
6.10 Time taken by each task when determining the NBB. . . 145
7.1 A wireframe of the simulated environment. . . 152
7.2 Visualisations of the robot exploring the environment. . . 153
7.3 Visualisations of the robot exploring the environment. . . 154
7.4 Portion of estimated information remaining over time. . . 155
LIST OF FIGURES xiii
7.6 The estimated effort of evaluated nodes at each iteration. . . 157
7.7 The estimated utility of evaluated nodes at each iteration. . . 158
7.8 Time taken by each task. . . 159
7.9 Detailed time taken by each task. . . 160
7.10 Time taken by each individual task. . . 161
B.1 Rays traversing the occupancy grid. . . 182
C.1 The Freiburg environment trajectories G (red), H (green), I (blue). . . 186
C.2 The Freiburg environment trajectories J (red), K (green), L (blue). . . 186
C.3 The Freiburg environment trajectories M (red), N (green), O (blue). . . 186
C.4 Cave trajectory summary (A, B, C). . . 187
C.5 Freiburg trajectory summary (D, E, F). . . 187
C.6 Freiburg trajectory summary (G, H, I). . . 188
C.7 Freiburg trajectory summary (J, K, L). . . 188
C.8 Freiburg trajectory summary (M, N, O). . . 188
C.9 Computation time at each iteration in Cave trajectory A. . . 189
C.10 Computation time at each iteration. . . 190
C.11 Computation time at each iteration. . . 191
List of Tables
4.1 Percentages of ground truth collected in each bridge site. . . 83
5.1 Example time taken for Na¨ıve frontier detection. . . 92
5.2 Correlation between the time taken to compute frontiers and... . . 117
5.3 Comparing computation time in seconds per 1000 cells for SBFD and CBFD.119 5.4 Minimum sizes of Ftfor |At| < |Ft−1|(d−1)/d to be true. . . 123
5.5 Order of complexity of each frontier detection algorithm. . . 123
5.6 Order of complexity of each algorithm without frontier grouping. . . 123
5.7 Assumptions and properties of frontier detection algorithms. . . 125
6.1 Time taken by each task. . . 141
6.2 Size of graph and number of nodes and edges evaluated. . . 141
7.1 Experiment parameters. . . 151
A.1 Results for Exploration in lab site 1. . . 171
A.2 Results for Exploration in lab site 2. . . 172
A.3 Results for Exploration in lab site 3. . . 172
A.4 Results for Exploration in lab site 4. . . 172
A.5 Results for Exploration in lab site 5. . . 173
A.6 Results for Exploration in bridge site 1. . . 173
A.7 Results for Exploration in bridge site 2. . . 173
A.8 Seconds spent performing each subtask during exploration in lab site 1. . . 174
A.9 Seconds spent performing each subtask during exploration in lab site 2. . . 174
A.10 Time (s) spent performing each subtask during exploration in lab site 3. . . 175
A.11 Time (s) spent performing each subtask during exploration in lab site 4. . . 175
A.12 Time (s) spent performing each subtask during exploration in lab site 5. . . 175
A.13 Time (s) spent performing each subtask during exploration in bridge site 1. 176 A.14 Time (s) spent performing each subtask during exploration in bridge site 2. 176 C.1 Correlation between the time taken to compute frontiers and... . . 192
C.2 Results for Cave trajectory A. . . 193
C.3 Results for Cave trajectory B. . . 193
C.4 Results for Cave trajectory C. . . 193
C.5 Results for Freiburg trajectory D. . . 193
C.6 Results for Freiburg trajectory E. . . 193 xiv
LIST OF TABLES xv
C.7 Results for Freiburg trajectory F. . . 193
C.8 Results for Freiburg trajectory G. . . 193
C.9 Results for Freiburg trajectory H. . . 194
C.10 Results for Freiburg trajectory I. . . 194
C.11 Results for Freiburg trajectory J. . . 194
C.12 Results for Freiburg trajectory K. . . 194
C.13 Results for Freiburg trajectory L. . . 194
C.14 Results for Freiburg trajectory M. . . 194
C.15 Results for Freiburg trajectory N. . . 194
Abbreviations
2D 2 Dimensional
3D 3 Dimensional
AXBAM Autonomous eXploration to Build A Map, system
BFS Breadth-First Search
C-space Configuration Space of manipulator
CBFD Change-Based Frontier Detection
DFS Depth-First Search
DOF Degrees of Freedom
EWFD Expanding Wavefront Frontier Detection
FFD Fast Frontier Detection
FOV Field Of View
FTFD Frontier-Tracing Frontier Detection
NBB Next Best Base location
NBV Next Best Viewpoint
NN Nearest Neighour
NNEA Nearest Neighour Exploration Approach
NNEA-B Nearest Neighour Exploration Approach with Backtracking
RGB-D Red Green Blue Depth camera.
RRT Rapidly-exploring Random Trees
SBFD State-Based Frontier Detection
SLAM Simultaneous Localisation And Mapping
WFD Wavefront Frontier Detection
WFD-INC Incremental Wavefront Frontier Detection
Nomenclature
General Formatting Style
f (· · ·) A scalar valued function
f(· · ·) A vector valued function [· · ·]T Transpose
| · | Absolute value
· Vector length and normalised vector
A\ B The set A without any elements that are also in B. Equivalent to
Bc∩ A.
N0 Natural numbers greater or equal to zero; e.g. 0, 1, 2, 3, ...
O(g(x)) Big O notation. f (x) = O(g(x)) means f (x) is bounded above
asymptotically by g(x). I.e. |f(x)| ≤ k × |g(x)|, for sufficiently large x, and some positive k.
Ω(g(x)) Big Omega notation. f (x) = Ω(g(x)) means f (x) is bounded below asymptotically by g(x). I.e. |f(x)| ≥ k × |g(x)|, for sufficiently large
x, and some positive k.
R2 The set of points in 2D Euclidean space; e.g. (1.2, -57.5).
R3 The set of points in 3D Euclidean space; e.g. (-3.4, 105.19, 8).
Θ(g(x)) Big Theta notation. f (x) = Ω(g(x)) means f (x) is bounded asymp-totically above and below by g(x). I.e. k1 × |g(x)| ≤ |f(x)| ≤
k2× |g(x)|, for sufficiently large x, and some positive k1 and k2.
Nearest Neighbour Exploration Approach
A The robot.
NOMENCLATURE xviii
A(q) The space taken up by the robot in configuration q.
C Configuration space.
Δθ The angle used to determine neighbouring configurations.
H(q) The information value of a configuration q.
Pt
f ree The set of known free-space at time t.
Pt
obs The set of known obstacles at time t.
Pt
unk The set of unknown space at time t.
Qa The set of candidate configurations under consideration by AXBAM.
Qtn The set of candidate configurations under consideration by NNEA at time t.
q A robot configuration, representing a vector of joint angles.
qt
curr The robot configuration at time t.
qtnbv The next best view configuration at time t.
t A variable representing time.
oTq
s The transform from map origin to sensor origin based on the robot configuration q.
τa The information threshold under which configurations will be dis-carded in the AXBAM algorithm.
τn The information threshold under which configurations will be dis-carded in the Nearest Neighbours phase of NNEA.
Frontier Detection Algorithms
At The active area of the observation at time t.
Amax The largest size of any possible active area.
Emax The largest size that any set of cells forming the boundary of any
S(Ot) could be.
E(Ot) The set of cells inS(Ot) that are on the edge of the map or adjacent to cells not inS(Ot).
Faa The set of known frontiers inside the active area under consideration.
Fnew The set of known frontiers that, when added to the set Ft−1, will make it become Ft.
NOMENCLATURE xix
Ft The set of known frontiers at time t.
Ft−1 The set of known frontiers at time t− 1.
M The set of cells in the map.
Mf ree The set of free-space cells in the map.
Ot The sensor observation made at time t.
ot The number of individual observations made as part of Ot.
Smax The largest size that any set of cells covered by the sensor could be.
S(Ot) The set of cells covered by the observation Ot.
Selecting the Next Best Base Location
A The set of valid attachment positions.
C The set of candidate attachment positions.
C(a, a0) The cost of reaching attachment position a given the robot begins at
a0.
dmax The maximum transition step the robot can make across a surface.
dmin The minimum transition step the robot can make across a surface.
ei,j An edge linking attachment position i and j.
F The set of frontiers.
H(a) A function returning the estimated information value of an attach-ment position a.
Mo The map of free and occupied space.
Ms The map of known surfaces.
pi,j,k A robot trajectory assuming the robot starts with the end effector at to attachment position i, the base affixed to attachment position
j, and the end effector will be moved to attachment position k.
qj,k A robot configuration “straddling” the base positions j and k.
rl The length of the robot.
rs The trustworthy range of the sensor.
s() The sampling policy which takes as argument a map of surfaces.
0T
NOMENCLATURE xx
τs The threshold under which an attachment position is considered un-safe.
U (g, s) The utility function taking as arguments a goal node g and start node s.
Glossary of Terms
Autonomous Without human intervention.
Base The footpad of the robot that is currently affixed to the surface. Binary Tree A tree data structure in which each node has at most two children. Bounding Box The smallest box, usually axis-aligned, that can be made to
con-tain a set of given points.
Candidate A node/position considered as the next potential position from which the robot should make new observation(s) of the environ-ment.
Cell A particular area of space in a discretised 2D map, usually indi-cated by an x and y index pair or coordinate. The same as a cell in a spreadsheet.
Climbing Robot A robot designed to be able to travel along vertical surfaces in some fashion.
Configuration-space A mathematically abstract space whose dimensions are the pa-rameters available for change by the robot. For example, a robot that has 2 joints would have a configuration space that is 2D. The axes of the space are the permissible values of that parameter. End Effector The device at the end of a robot manipulator which with the robot
interacts with the environment.
Environment The area or volume of space that the robot will operate in. Ferromagnetic Made of metals to which magnets are attracted.
Footpad A link on the end of the robot that affixes itself to the surface. xxi
GLOSSARY OF TERMS xxii
Freespace Space that is known to be empty of obstacles.
Frontier The boundary between known free-space and unknown space. Greedy An algorithm in computing is considered greedy if it makes
deci-sions based on short time-horizons, including as little as a single time-step.
Holonomic An object (in the context of this thesis, a robot) is holonomic if its kinematic properties would allow it to freely move in any direction from a given position.
Information A measure of uncertainty in the state of an environment/model. Joint Effort The sum of the difference in joint angles between two or more
poses.
K-d Tree A tree for storing points in k-dimensional space. Kinematic Chain A configuration of rigid bodies connected by joints. Kinematics The description of the motion of a system of objects.
Known Space Space that is either known to be empty of obstacles, or known to contain an obstacle.
Manipulator Robot A series of motors connected by joints, usually with one end fixed in place and the other end affixed with a tool or gripper.
Map A representation of the environment, typically updated,
main-tained and used by the robot.
Occupancy Map A discretised grid representation of the environment, made up of cells that store values representing the probability that that position in space contains an obstacle.
Octree A compact method for storing a 3D occupancy map. The grid is stored as a tree so that when all eight children of a parent node have the same value, they can be deleted and the parent holds the value instead.
Obstacle An impassable object.
Operator A person in charge of controlling or monitoring a robot as it per-forms a task.
GLOSSARY OF TERMS xxiii
Pose The position and configuration of an object such as a robot, robot joint, end effector or sensor.
Quadtree A compact method for storing a 2D occupancy map. The grid is stored as a tree so that when all four children of a parent node have the same value, they can be deleted and the parent holds the value instead.
Ray-cast/Ray-trace Techniques for calculating the path of a ray through a grid or set of objects to determine which it interacts with.
Robot A machine able to perform actions based on information it collects about the environment around it.
Surface Map A map of 3D surface information.
Teleoperation Operation of a machine from a distance by a human operator. Triangle Mesh A method for representing surfaces as a set of triangles connected
by their edges and vertices.
Tether A cable connecting the robot to either a control station, a power source, or a larger structure for safety, or a combination of these. Unknown Space Space that whose obstacle status is not known. It might or might
not contain an obstacle.
Viewpoint The position and orientation of a sensor in space, often as a result of a particular robot configuration, which determine what portion of the environment is covered by the sensor field of view.
Voxel A particular volume of space in a 3D discretised map, usually represented by an (x,y,z) coordinate.
